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2021 IMO Shortlist
A1
A1
Part of
2021 IMO Shortlist
Problems
(1)
set with c+2a>3b
Source: ISL 2021 A1
7/12/2022
Let
n
n
n
be a positive integer. Given is a subset
A
A
A
of
{
0
,
1
,
.
.
.
,
5
n
}
\{0,1,...,5^n\}
{
0
,
1
,
...
,
5
n
}
with
4
n
+
2
4n+2
4
n
+
2
elements. Prove that there exist three elements
a
<
b
<
c
a<b<c
a
<
b
<
c
from
A
A
A
such that
c
+
2
a
>
3
b
c+2a>3b
c
+
2
a
>
3
b
.Proposed by Dominik Burek and Tomasz Ciesla, Poland
algebra
IMO Shortlist
2021
A1
ISL 2021